Cosine of 225 Degrees
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Theorem
- $\cos 225 \degrees = \cos \dfrac {5 \pi} 4 = -\dfrac {\sqrt 2} 2$
where $\cos$ denotes cosine.
Proof
\(\ds \cos 225 \degrees\) | \(=\) | \(\ds \map \cos {360 \degrees - 135 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \cos 135 \degrees\) | Cosine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\frac {\sqrt 2} 2\) | Cosine of $135 \degrees$ |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles